There appears to be a 2.7V zener, maybe this is used as a reference? There are some very stable zener diodes. An internal band gap reference in the IC might also have enough accuracy, especially if it's calibrated after assembly.
0.1% isn't that great for 4.5 dgits, at 19.999V, the uncertainty would be +/- .020V, so the last digit is garbage, and I wouldn't trust the second to last digit to be very accurate either (if it's 5, it might be between 3 and 7). You would need something like a 16-bit ADC for that kind of resolution, but that assumes that all those digits are actually real. Given the accuracy, they might as well use a 12 bit ADC or even 10 bit DAC (just use some random number or averaging for the extra digit). Without a datasheet, I wouldn't assume anything.
My guess is that the mystery chip is either a modern equivalent of the ICL710x, or some sort of 8-bit micro (I'm sure there are micros with 16-bit ADC).
One issue is if it needs a power supply that's isolated from the unknown voltage, I really hate this with many digital panel meters, and tend to prefer analog (if I don't need accuracy) or rolling my own with a MCU for this reason.